Revealing a deep connection between factorization and saturation: New insight into modeling high-energy proton-proton and nucleus-nucleus scattering in the EPOS4 framework

It is known that multiple partonic scatterings in high-energy proton-proton ($pp$) collisions must happen in parallel. However, a rigorous parallel scattering formalism, taking energy sharing properly into account, fails to reproduce factorization, which on the other hand is the basis of almost all $pp$ event generators. In addition, binary scaling in nuclear scatterings is badly violated. These problems are usually ``solved'' by simply not considering strictly parallel scatterings, which is not a solution. I will report on new ideas (leading to EPOS4), which allow recovering perfectly factorization, and also binary scaling in $AA$ collisions, in a rigorous unbiased parallel scattering formalism. In this new approach, dynamical saturation scales play a crucial role, and this seems to be the missing piece needed to reconcile parallel scattering with factorization. From a practical point of view, one can compute within the EPOS4 framework parton distribution functions (EPOS PDFs) and use them to compute inclusive $pp$ cross sections. So, for the first time, one may compute inclusive jet production (for heavy or light flavors) at very high transverse momentum ($p_{t}$) and at the same time in the same formalism study flow effects at low $p_{t}$ in high-multiplicity $pp$ events, making EPOS4 a full-scale ``general purpose event generator''. I discuss applications, essentially multiplicity dependencies (of particle ratios, mean $p_{t}$, charm production) which are very strongly affected by the saturation issues discussed in this paper.